I watched your video and read your description here - thanks, both were really helpful.
A short while ago I bought a 1993 US Musicman Stingray bass for a really good price - it is all original except the bridge ... it seems the seller dismantled the bass to refinish it (which, thankfully wasn't done!) and mislaid the bridge - the bridge would have been the one with string mutes. I took it all apart when I got it and it is legit - it even has holes in the body under where the screws for the string mutes would have been. It really is a lovely bass to play but the bridge was the Sterling type just like yours. Unfortunately it's not possible to get an authentic bridge from Musicman (if anyone knows different, please let me know!).
Taking confidence from your YouTube video and this article, I decided to buy the string mutes (from Bassdirect) and fit them. I had to drill holes in the bridge as you did, but also used a tap to create a screw thread in the holes in the bridge for the screws that came with the kit - I bought a tap and die set from Amazon for under £30 (US units rather than metric) and had to do a bit of testing before I discovered which was the correct size. The screws fit perfectly and it now look pretty much like the original bridge would have looked.
It now looks great - and it plays and sounds superb!
Thanks for your video and post here.